PSY 512 Curvilinear Regression - Self and Interpersonal ...

PSY 512: Advanced Statistics for 1/2/2016
Psychological and Behavioral Research 2 1

Introduce the idea of curvilinear
regression
Polynomials

• Quadratic
• Cubic

The estimated residuals provide the best method for
checking for curvilinear associations
In a residual plot, you are looking for curvature

To account for curvature,we can perform 1/2/2016
something called “polynomial regression” 2
which consists of fitting a polynomial (a
quadratic or cubic typically) instead of a line
Linear model

• Y = A + β1X + e

Quadratic model (1 bend in the data)

• Y = A + β1X + β2X2 + e

Cubic model (2 bends in the data)

• Y = A + β1X + β2X2 + β3X3 + e

The higher the order of the polynomial, the
more curvature for which it can account

In general, choose the LOWEST order
polynomial possible (e.g., prefer linear to
quadratic…quadratic to cubic)
This is aimed at (1) “Occam’s razor”
meaning that simpler models are preferred
and (2) the higher the order of the
polynomial term, the more parameters to
estimate (it is easier to estimate a few
parameters than it is to estimate many)

The regression output provides a formal
method for selecting the appropriate
polynomial

• This method typically agrees with looking at the
residual plot

The regression output provides p-values for
each term in the regression
These p-values can be used to guide
decisions about which polynomial terms to
include in the model

Begin by fitting the cubic model 1/2/2016
• If the cubic term is significant,use the cubic 3

model
If the cubic term is NOT significant,remove it, and
rerun the model
• Look to see whether the quadratic term is

significant
If the quadratic term is not significant,remove it,
and rerun the model (i.e.,simple linear regression)

Time spent on work
tasks across time
Music made
available at work
during weeks 2 and 3
Music removed
during week 4
Music reinstated
during week 5

Time spent on work
tasks across time
Music made
available at work
during weeks 2 and 3
Music removed
during week 4
Music reinstated
during week 5

Positive affect across 1/2/2016
time 4
Music made
available at work
during weeks 2 and 3
Music removed
during week 4
Music reinstated
during week 5

Positive affect across
time
Music made
available at work
during weeks 2 and 3
Music removed
during week 4
Music reinstated
during week 5